Aircraft: A319
Phase of flight: Taxi
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown

Three minutes after landing in Richmond; VA; while taxiing to our assigned Gate; we shut down Engine 2; and continued to single-engine taxi; per Company Policy. As we approached the gate the First Officer (Pilot Monitoring) and I (Pilot Flying); confirmed that all ground equipment was outside the footprint of the ramp area for the gate. We approached at a taxi speed of approximately 5 knots; while being directed by the Marshaller; with a wing walker on the left and a wing walker on the right. At approximately 5 to 10 feet prior to reaching the parking position; the aircraft main tires met with a significant change in the ramp surface level where the ramp surface changes from asphalt to a concrete pad. In other words; there seemed to be a significant 'lip' from the edge of the asphalt to the edge of the concrete parking pad used for parking aircraft. When the aircraft main tires reached this point of transition from the asphalt to the concrete at a speed of approximately 5 knots or less; the aircraft stopped its forward progress and began to move backwards; whereupon the aircraft brakes were applied; and the aircraft stopped. At this point; the aircraft was not yet at the correct parking position. The Marshaller continued to direct us to move forward and thrust was increased on Engine 1 to attempt to move forward across the 'lip' between the asphalt ramp and concrete pad. With only Engine 1 operating; we were not able to move the aircraft forward to the correct parking position without using more than the maximum breakaway thrust of 40% N1. An announcement was made to the passengers and instructions given to remain seated with seat belts fastened until Engine 2 was restarted and the aircraft was properly positioned at the gate. With the aircraft stopped and the parking brake set; we signaled to the Marshaller that we were starting Engine 2. After starting Engine 2; the Marshaller began to direct us to the proper parking position. With both engines running; maximum breakaway thrust on both engines (and possibly more) was needed to move the aircraft across the 'lip' between the asphalt portion of the ramp area and the concrete parking pad to the proper parking position as directed by the Marshall[er]. The event occurred due to a taxi speed not adequate to allow the aircraft to transition from the asphalt portion of the ramp to the concrete portion of the ramp used as the parking pad. Following this event; after speaking with a Company Customer Service Representative in Richmond; it was learned that repair work to the ramp area in question had been performed on more than one occasion; due to similar events occurring with other aircraft parking at Gate. It is evident that this may be an ongoing issue and concern; at least at this particular gate in Richmond. In addition; this flight segment to Richmond departed late due to an earlier flight we operated in arriving over one hour late. While sensing a need to get the customers to the gate after landing in Richmond; because the flight departed late and arrived in Richmond late (i.e. 'rush to comply'); excessive thrust was used in an attempt to get the aircraft to the parking position and avoid any further delay.Following this event; after careful review and consideration; I am concerned that the course of action taken by me (Pilot Flying) was not in the best interest of safety; especially with regard to the protection of Company personnel and equipment. While being directed by the marshaller toward the parking position; and while attempting to taxi across the 'lip' between the asphalt portion of the ramp and the concrete parking pad using maximum breakaway thrust (and possibly an exceedance of maximum breakaway thrust) first with one engine operating; and then with both engines operating; serious injury to ramp personnel; FOD damage to the aircraft engines; and damage to ground equipment in front and behind the aircraft; could have occurred. Thankfully; no personnel were injured; no FOD damage occurred in either engine; nor was there any damage to ground equipment in front of or behind the aircraft.In the future; the primary suggestion to myself; or anyone else; to avoid a reoccurrence of this event; or any similar event; is as follows: When an amount of thrust equal to maximum breakaway thrust is not sufficient to move the aircraft into the proper parking position:1. Do not exceed maximum breakaway thrust in an attempt to reach the parking position.2. Set the parking brake.3. Coordinate with Operations/Ground Crew to be towed to the parking position.4. If required by Company or Local Policy/Procedure; or if requested by Operations or the Ground Crew; shut engine(s) down prior to towing. A319 Captain reported a 'lip' approaching his gate as the asphalt ramp transitions to the concrete parking pad. The crew is single engine taxing and is unable to cross the 'lip'. The second engine is started and 40% N1 is required to cross the 'lip'. The reporter believes that he may have jeopardized safety by using this must thrust in the gate area in order to move the aircraft to the correct position.